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Physical Review D 82 (2010) 063510
No-boundary measure in the regime of eternal inflation
J. Hartle, S.W. Hawking1, T. Hertog2, 3

The no-boundary wave function (NBWF) specifies a measure for prediction in cosmology that selects inflationary histories and remains well behaved for spatially large or infinite universes. This paper explores the predictions of the NBWF for linear scalar fluctuations about homogeneous and isotropic backgrounds in models with a single scalar field moving in a quadratic potential. We treat both the spacetime geometry of the universe and the observers inhabiting it quantum mechanically. We evaluate top-down probabilities for local observations that are conditioned on the NBWF and on part of our data as observers of the universe. For models where the most probable histories do not have a regime of eternal inflation, the NBWF predicts homogeneity on large scales, a spectrum of observable fluctuations with a small non-Gaussian component, and a small amount of inflation in our past. By contrast, for models where the dominant histories have a regime of eternal inflation, the NBWF predicts significant inhomogeneity on scales much larger than the present horizon, a Gaussian spectrum of observable fluctuations, and a long period of inflation in our past. The absence or presence of non-Gaussianity in our observable universe therefore provides information about its global structure, assuming the NBWF.
1 :  DAMTP/CMS - Department of Applied Mathematics and Theoretical Physics / Centre for Mathematical Sciences
2 :  APC - UMR 7164 - AstroParticule et Cosmologie
3 :  International Solvay Institutes
Physique/Astrophysique/Cosmologie et astrophysique extra-galactique

Planète et Univers/Astrophysique/Cosmologie et astrophysique extra-galactique

Physique/Physique des Hautes Energies - Théorie

Physique/Relativité Générale et Cosmologie Quantique
Quantum cosmology – Quantum gravity – Origin and formation of the Universe – Particle-theory and field-theory models of the early Universe
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